常微分方程边值问题的高阶三对角OCI差分法  

HIGH ORDER TRIDIAGONAL OCI DIFFERENCE SCHEME FOR ORDINARY DIFFERENTIAL EQUATIONS WITH BOUNDARY VALUES

作　　者：彭点云[1] 

机构地区：[1]西南物理研究院,成都610041

出　　处：《计算物理》1993年第4期413-421,共9页Chinese Journal of Computational Physics

摘　　要：本文给出了二阶线性常微分方程两点边值问题(ODETPBVP)的高阶差分格式构造的基本思想,推导出六阶三对角OCI差分格式,并对端点有奇异性的方程进行了极限值处理,消去了奇异性,对边界层问题采用了非均匀网格上的六阶三对角OCI差分格式。通过大量的数值比较实验表明,这种高阶三对角OCI差分格式能很好地求解奇异性问题,固有不稳定性问题,奇异摄动问题,对生不稳定性问题和振荡性问题。This paper presents basic idea to construct high order difference schemes for linear two order ordinary differential equations with boundary values. A six order tridiagonal OCI difference scheme is deduced and the singularity at ends of interval are treated by means of limited values. A six order tridiagonal OCI difference scheme on non-uniform mesh is adopted for layer problems. A large number of numerical experimental results show that this high order tridiagonal OCI difference scheme can solve singular problems, inherent instability problems, dichotomous instability problems, singular perturbation problems and oscillating problems very well.

关 键 词：常微分方程 边值问题 差分法 

分 类 号：O411.1[理学—理论物理]